A projectile is launched from the ground. Its flight is an arc, and it lands on the roof of a building. Its initial velocity is 85 m/s at an angle of 60 degrees. Its total flight time is 9.51 seconds. How high is the building?

Hello! This is a physics kinematics problem, therefore we want to use one of our kinematics equations. The equation that we should use is y(f)=y(0)+v(0)t+((1/2)a(t^2)). Where y(f) represents the final height we are looking for, y(0) represents the initial height on the ground (0 meters), v(0) represents the initial velocity in the y direction, t represents the flight time, and a represents the acceleration in the y direction due to gravity (-9.8m/s^2). Since we are looking for the height we know that everything is in terms of the y direction (aka. vertical direction).

Since our initial velocity is given as a magnitude of the two velocities, it is composed of component velocities in the x direction and y direction. We need to find the component in the y direction since we are looking for height. This can be achieved through trigonometry. The angle 60 degrees is given as well as the initial magnitude of the velocity. If we draw a picture of the initial velocity as a triangle, it can be observed that the initial angle is opposite the vertical side of the triangle. Therefore the vertical component, or y component of the velocity is the initial velocity (85m/s) multiplied by the sin of the angle (60 degrees).

After this we can plug everything into our equation above to find the initial height of the building that we are looking for.

y(f)=0+((85)(sin60)(9.51))+((1/2)(-9.8)(9.51^2))

Our answer by using our calculator is 256.89551 meters or approximately 257 meters. I hope this was helpful! :)

Dec 17th, 2014

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